Large volume metrology measurements are conducted at every major phase of alignment and integration of large scale extraterrestrial instruments, for example, the Integrated Science Instrument Module which forms the main payload of the James Webb Space Telescope at NASA Goddard Space Flight Center. Placement of components within large scale assemblies may require precisely locating metrology targets and predicting locations of targets that may be out of view. A network of both ambient and cryogenic metrology measurements may be used to verify that components of the large scale extraterrestrial instrument and ground support equipment conform to the predicted position and orientation at various integration and alignment states. The combining of multiple location and orientation measurements and their uncertainties from the network of different metrology instruments may be accomplished using various data gathering and data analysis tools or programs. The resulting measurements and their uncertainties constitute a metrology calibration database for a particular test configuration.
Best-fit transformations are routinely used in metrology to adjust the position and orientation of points, objects, coordinate systems, and measurement instruments. A best-fit spatial-transformation, however, transforms nominal targets without regard to the uncertainty in those targets. In principle, it is possible to apply hundreds of transformations back-and forth between common targets in two different databases with only negligible round-off error when using double precision operations. In practice, however, there is an accuracy penalty associated with applying a transformation to common measured targets that is dependent on the uncertainty in those targets.
Monte Carlo simulations are routinely used in the aerospace and other industries to explore the sensitivity in the output of complex systems by iteratively varying the input parameters within statistical limits. These complex systems can be mathematical or physical in nature and usually contain multiple coupled degrees of freedom where closed-form solutions are difficult or impossible to obtain. A Monte Carlo approach is well suited to characterizing the sensitivity of transformed 3D-points because of the nonlinearity associated with a composite rotation matrix.